Question: Integrals e^2x

Answer:

The anti derivative of e^2x is a function of x whose derivative is e^2x.

It is known that,

\begin{align} \frac {d}{dx} (e^{2x}) = 2e^{2x} \end{align}

⇒ \begin{align} e^{2x} =\frac {1}{2} \frac {d}{dx}(e^{2x}) \end{align}

∴ \begin{align} e^{2x} = \frac {d}{dx}\left(\frac {1}{2}e^{2x}\right) \end{align}

Therefore, the anti derivative of e^2x

\begin{align} e^{2x} \;is \frac {1}{2}e^{2x} \end{align}

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